Physics 4610 Syllabus

Spring semester, 2016

Meeting time: MWF 12:30–1:20Instructor:Daniel V. SchroederOffice hours: MWF 11:30–12:00 and Mondays 1:30–2:20. I will also be available later on
most MWF afternoons, and I can come in early MWF mornings if you make an appointment. I will not
be on campus most Tuesdays and Thursdays.Office: SL 208Phone: 801-626-6048 (note that I check email much more often than voicemail)Email: dschroeder at weber dot eduCourse web site:http://physics.weber.edu/schroeder/quantum/

Text: I will hand out reading materials (and post them on the course web site) for much of
the semester. I also recommend that you obtain and use a standard undergraduate quantum
mechanics textbook such as David J. Griffiths, Introduction to Quantum Mechanics, second edition
(Pearson Prentice Hall, 2005).

Why study quantum mechanics?

There are many practical reasons to study quantum mechanics, since
it underlies and illuminates so many aspects of physics, chemistry,
and modern technology. Furthermore, the mathematical tools of quantum
mechanics (calculus, linear algebra, Fourier analysis) are used
in a much wider array of scientific disciplines. More generally,
studying quantum mechanics will continue to build your skills
in problem solving and quantitative reasoning.

On a less practical
level, many students are simply curious about quantum mechanics,
since it makes such outrageous assaults on our common ways
of thinking about the world. Personally, I also find it
highly satisfying to “understand” nature at the deepest possible
level. But perhaps most importantly, quantum mechanics forces
us to think in new, unfamiliar ways: to develop intuition for the
counter-intuitive. It is this kind of experience that constitutes
education in the truest sense. Thus I hope you will find your study
of quantum mechanics to be not merely informative, but also liberating.

Summary of topics

This course will treat the theory of quantum mechanics at a more advanced level than you saw in
your Introductory Modern Physics (2710) course. While this is mostly a course in quantum theory,
I will also try to introduce some applications as time allows. The course will be divided into four
major sections:

Wave mechanics in one dimension. We will begin with the quantum mechanics of a single,
structureless particle moving in one dimension. In this restricted and reasonably familiar context,
we will work to obtain a general understanding of wavefunctions, quantum uncertainties, and energy
quantization. We will use one-dimensional model systems to understand trapped
particles, vibrating molecules, electrons in molecules and solids, and tunneling.

The general theory of quantum mechanics. Next we will generalize quantum theory to
include particles moving in more than one dimension, systems of more than one particle, and
particles with internal structure. The new concept of entanglement arises in all of
these more complicated systems. To encompass these systems we will use the powerful mathematical
language of vector spaces, linear operators, and eigenvectors, and eigenvalues.

Three-dimensional systems. We continue with an in-depth look at the quantum mechanics of
a single particle in three dimensions, emphasizing the special case of spherically symmetric
systems in which angular momentum is conserved. The most important (but not the only) application
will be to a particle trapped in a Coulomb potential, that is, the hydrogen atom.

Spins and quantum information. Finally we turn to mathematically simpler (but
more abstract) systems in which it is the internal structure (usually spin or polarization)
that is of primary interest. Besides the traditional applications to atomic physics,
we will use this context to explore entanglement in some depth, as illustrated by Bell’s
theorem, quantum cryptography, and quantum computing.

Course policies

As mentioned above, I will try to hand out reading materials throughout most of the semester.
I will expect you to read these handouts before coming to class, and to participate in class
discussions. At this point in your education it is no longer acceptable to just sit back and listen.

I am not planning on doing a lot of lecturing. Instead we will spend class time on questions,
examples, activities, and discussion.

We will have 12 problem sets. As usual in a theoretical physics course, this is
where most of the learning will take place. The problem sets are not tests, and you are not expected
to be able to solve every problem correctly the first time, on your own. On the other hand, you
won’t learn anything if you rely on others too heavily as you work the problems. So here are the
rules:

Spend at least ten minutes on each problem (or part thereof), making a good-faith effort to solve
it yourself, before you seek help on it from anyone else.

Do ask me or a classmate for a hint if you are still stuck on a problem after 10 or 15 minutes.
You may also ask for hints from other WSU faculty members. When asking for a hint, it’s usually helpful
if you first explain what you do already understand.

When you obtain assistance from someone, acknowledge that person by name in your writeup of the
problem. Be specific about exactly how that person helped: “Special thanks to L. Meitner for
reminding me that neutrons are fermions.” Please don’t feel embarrassed
for having obtained help. This is absolutely routine in academia, but we always acknowledge the
assistance we receive.

Whether or not you obtain assistance in solving a problem, be sure to check your answers with
classmates or with me. If this check results in a revision to your solution, include an acknowledgment
as described above.

Never look at anyone else’s written solution before turning in your own. This includes
any and all solutions written by me or by other instructors or students or anyone else. Do not tempt
your classmates by showing them your own written solutions. Comparing answers (including
intermediate results) is encouraged but comparing entire solutions is not allowed.

Never seek help from internet sites, or from anyone not affiliated with WSU, without advance permission.

Naturally, you may consult any source you like after you have turned in your own solutions.

If you are ever in doubt about the interpretation of these policies, ask.

Take pride in your work! Your final written solutions to problem sets should be clearly
presented and fully explained, at a level of detail that any of your classmates could read and
understand. While your solutions needn’t be of publication quality, they should be reasonably legible and
well organized.

Problem sets must be submitted on paper, not electronically. Please leave room in
the margins for my comments.

Late problem sets will be marked down by 1/3 of the total credit for each day or partial day. However, only
your 11 highest problem set scores (out of 12 total) will count toward your final grade,
so you may miss one problem set without penalty. This policy should provide enough
flexibility to accomodate most illnesses, family emergencies, unexpected romances,
and the like. In the case of extended illness or other long-term emergency, please
consult with me at the earliest opportunity.

We will have three closed-book midterm exams, each with a time limit of 90 minutes,
given in the Science Testing Center. You will have a 47-hour window (minus those
hours when the testing center is closed) in which to
take each exam.

At the end of the course you will complete a final project that will be based on an
article of your choice from the American
Journal of Physics or a similar journal. In brief, you
will choose an article on a topic in quantum mechanics that interests you, reproduce the
calculations (or a substantial portion of them, perhaps with some modifications) in the article, and then explain the article to
your peers
in a 15-minute presentation and in a formal paper (written up as a “note”
commenting on the original article). Not all articles are suitable for this assignment
so please obtain my approval of your choice before you begin any significant work.
Also please consult with me regarding the type of outside help that
might be appropriate as you
carry out your project work; in all cases you must explicitly give credit to each
source that you relied upon, explaining how you relied upon it. The presentations will take
place during our scheduled final exam time: Wednesday, April 27, 1:00 to 2:50 pm.

Grades

I will calculate your final grades using the following percentage weights:

Problem sets (11 @3%)

33%

Midterm exams (3 @15%)

45%

Class participation

8%

Final project

14%

Miscellaneous

In the event of a snow day or other campus shutdown, please check your email as soon
as you can for specific instructions regarding this course. Obviously I will not require
you to turn in a problem set or take a test on a day when the campus is closed, but otherwise
you should assume that all deadlines are still in effect unless I explicitly modify them.
It is your responsibility to make sure I have your correct email address.

Any student requiring accommodations or services due to a disability must contact
Services for Students with Disabilities (SSD) in room 181 of the Student Service Center.
SSD can also arrange to provide course materials (including this syllabus) in alternative
formats if necessary.

Academic dishonesty, though rare, occasionally does occur in physics classes, so the
following policies are necessary. Inappropriate collaboration or other dishonesty on
homework will result in a zero grade for that problem set on the first occurrence
and failure in the course thereafter. Dishonesty of any sort on a test or final project
will result in automatic failure in the course. In serious cases, evidence of dishonesty
may also be presented to the appropriate hearing committee for possible further sanctions.